Frequency conversion of laser radiation based on harmonic generation is generally known. As basic examples, frequency doubling or tripling can be obtained with second or third order harmonic generation (SHG, THG) using solid optically non-linear crystals. For conversions to higher frequencies, towards the XUV and soft x-ray spectral region, high order harmonic generation is realized (n-th harmonic generation, n>5) using non-linear processes in gas targets. High order harmonic generation has been described by T. Brabec and F. Krausz in “Reviews of Modern Physics” (vol. 72, 2000, p. 545 to 591, in particular p. 571). While SHG or THG crystals have a large conversion efficiency of up to 50%, gas targets have an extremely low conversion efficiency in the range of 10−9 to 10−7 for the XUV (near 13 nm or below).
Even those low conversion efficiencies were generated only with complex and expensive laser amplifier systems. Those high-energy systems necessarily reduce the pulse repetition rate by several orders of magnitude, typically to the kHz range. Several scientific experiments and technological processes benefit from HHG radiation with increased repetition rate. Exemplarily, in XUV spectroscopy weak signals have to be accumulated for days with the current low-repetition laser systems. The collecting (integration) time can be shortened by a factor of up to 1000 by providing the HHG radiation at the full, original repetition rate.
Previous attempts to increase the conversion efficiency were based on increasing the gas density of the gas target or the so-called quasi phase matching (QPM) in hollow fibers. Both techniques can be applied to a limited extent only, as the increased gas density can reduce the HHG efficiency due to increased absorption and QPM is not well-adapted for gas targets.
Another technique of increasing the conversion efficiency is based on intra-cavity generation of pulsed HHG radiation in the extreme ultraviolet spectral range as described in US 2006/0268949 A1 (see also C. Gohle et al. in “Nature”, vol. 436, 14 Jul. 2005, p. 234; or R. J. Jones et al. in “Physical Review Letters”, vol. 94, 2005, p. 193201-1). The HHG radiation is provided inside a resonator by a harmonic generation process in an optically non-linear medium, like a gas jet, which is irradiated with laser light pulses. The laser light pulses are provided in a resonant cavity wherein, due to a coherent enhancement (coherent addition), the laser light pulses have a peak intensity which is large enough to drive the harmonic generation process. The enhancement is obtained by a precise adjustment of the resonant cavity and a driving laser source relative to each other so that high intensity laser light pulses are provided while preserving the repetition rate of the driving laser source.
The aforementioned conventional technique of generating HHG radiation in an external cavity has two limitations which have restricted the further development of this technique. The limitations are related to the enhancement factor of the resonant cavity and dispersion effects in the resonant cavity. In particular, the coherent addition requires that the pulse shape is maintained after each resonator round trip.
First, the factor of enhancement (average power circulating inside the resonant cavity versus incident average power) can be limited by intrinsic cavity losses, like mirror absorption, scattering in air, etc. With the conventional resonant cavity, the maximum achievable enhancement factor is given by P=1/(1−r2), wherein r is the product of all mirror reflectivities and additional scattering losses in the resonant cavity.
Second, the enhancement is constrained to frequency components of the incident laser pulses from the driving laser source that fulfill the requirement of vanishing dispersion inside the resonant cavity. If this condition is not met, spectral clipping will occur, resulting in circulating pulses with a longer pulse width. Despite recent advances in mirror coating and characterization techniques, this criterion is still a factor that limits enhancement and the bandwidth supported by the resonant cavity. Due to this bandwidth-limitation, only pulses longer than about 30 fs have been used in conventional techniques.
Due to the above limitations (intra-cavity circulating power, pulse duration), the application of the conventional technique for generating pulsed HHG radiation is restricted to relative low intensities with pulse durations in the fs-range. However, for the expected applications of XUV pulses, driving pulses with a sub-10 fs duration are required, in particular for producing attosecond pulses of coherent radiation by harmonic generation.
Another general disadvantage of the conventional radiation sources for generating pulsed HHG radiation in an external cavity is given by the fact that a combination of the driving laser source and the external resonant cavity, as described, e.g., in US 2006/0268949 A1, represents a complex optical set-up, which requires an extensive and time-consuming adjustment. Therefore, the application of the conventional radiation sources in a practical device, like a microscope or lithography apparatus, is restricted.
It could therefore be helpful to provide an improved radiation source for providing pulsed HHG radiation which is capable of overcoming limitations of the conventional techniques. In particular, the radiation source is to be capable of generating pulsed radiation in the wavelength ranges of UV to XUV or even to X-ray wavelengths with increased intensity, reduced pulse duration and/or increased repetition rate. Furthermore, it could be helpful to provide an improved method for providing pulsed HHG radiation which is characterized by an increased intensity and/or reduced pulse duration, while preserving the repetition rate of the driving laser. It could further be helpful to provide the improved radiation source or radiation generating method with an optical set-up having a reduced complexity, which in particular allows the generation of the pulsed coherent radiation under practical conditions with reduced requirements as to adjustment and maintenance.